Women can experience a few different kinds of orgasms related to different parts of the female anatomy — clitoral, G-spot, vaginal, cervical, and more. For the vast majority of women a clitoral or G-spot orgasm isn't difficult to achieve, while cervical orgasms are pretty rare since most women find cervical contact somewhere between uncomfortable and unbearable.
But the vaginal orgasm? That's one that a lot of men are chasing, and the one that is often said to be easier to achieve with size. In fact, one study looked at that question and found a connection… but it's a bit more nuanced than just "bigger penis = more vaginal orgasms."
The 2012 study in Scotland surveyed more than three hundred women and their experience with penis size and vaginal orgasms. It concluded:
Women who prefer deeper penile–vaginal stimulation are more likely to have vaginal orgasm, consistent with vaginal orgasm evolving as part of a female mate choice system favoring somewhat larger than average penises.
Note that the researchers did not conclude that longer penises cause more vaginal orgasms for all women — just in women that prefer deeper penetration and stimulation. And even then, only drawing conclusions about "somewhat larger than average penises".
But that leads to the question of "how many women is that"? Of the women in the study group, just 17% reported that a longer penis made them more likely to orgasm. Thirty percent said it made no difference to them, and 30% said the never or rarely experience vaginal orgasms from penile penetration. And three percent actually reported that they were less likely to have an orgasm when a longer penis was involved.
So with roughly 1-in-6 women, penis size can make a positive difference in their ability to achieve vaginal orgasm. For the rest it makes little to no difference. Some of that may come down to anatomical variations, as women have the same sort of distribution in vaginal size as men do in penis size. Most vaginas are around average, but a small portion are significantly larger while roughly as many are smaller. And there's no way to predict how much capacity she might be packing.
Since the vast majority of women don't find penis size that important to achieving vaginal orgasm, what's a man to do? Start by accepting that size isn't the be-all, end-all for most women. There are a variety of positions that can make sex with a longer penis work better for both of you, and depth limiters can help expand that variety. And, of course, loads of foreplay to make it easier — not to mention the clitoral stimulation that most women find much more helpful in reaching orgasm than just a thrusting penis.
More often than not, technique is going to be far more important to sexual satisfaction than size.